Convection in a differentially heated rotating spherical shell of Boussinesq fluid with radiative forcing
Date
2012-12-01
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Abstract
In this study we investigate the
flow of a Boussinesq
fluid contained in a rotating, differentially heated spherical shell. Previous work, on the spherical shell of Boussinesq fluid, differentially heated the shell by prescribing temperature on the inner boundary
of the shell, setting the temperature deviation from the reference temperature to vary
proportionally with -cos 20, from the equator to the pole. We change the model to
include an energy balance equation at the earth's surface, which incorporates latitudinal solar radiation distribution and ice-albedo feedback mechanism with moving ice
boundary. For the
fluid velocity, on the inner boundary, two conditions are considered:
stress-free and no-slip. However, the model under consideration contains only simple
representations of a small number of climate variables and thus is not a climate model
per se but rather a tool to aid in understanding how changes in these variables may
affect our planet's climate.
The solution of the model is followed as the differential heating is changed, using the pseudo arc-length continuation method, which is a reliable method that can
successfully follow a solution curve even at a turning point.
Our main result is in regards to hysteresis phenomenon that is associated with
transition from one to multiple convective cells, in a dfferentially heated, co-rotating
spherical shell. In particular, we find that hysteresis can be observed without transition
from one to multiple convective cells. Another important observation is that the
transition to multiple convective cells is significantly suppressed altogether, in the
case of stress-free boundary conditions on the fluid velocity. Also, the results of this
study will be related to our present-day climate.
Description
Keywords
Convection, Hysteresis, Cusp bifurcation, Albedo, Hadley cell, Radiative forcing, Spherical shell, Boussinesq fluid